Before we conclude, let us make some general comments. The reader may have observed a pattern here. We can start with a \((\Delta ,l)\)  primary, \(S^{\Delta }_{a_1a_2...a_l}\)  and ask, what kind of (large) gauge transformation is it potentially connected to? If, for the time being, we subscribe to the rule of thumb that null state corresponds to large gauge transformation, then this problem can be completely solved using the results of [1]}. What we have to do is to look for \((\Delta ,l)\)  primary descendant or null-state. The null-state should have dimension \(\Delta \)  and spin \(l\)  because we have to add the null-state to \(S^{\Delta }_{a_1a_2...a_l}\) . Let us do it for a \((\Delta =0,l=2)\)  primary, which could be a sub-leading soft-graviton As we have already discussed in section (), according to [1]} there are three types of primary descendants : Type-1, type-2 and type-3. Now one can easily check that a \((\Delta =0,l=2)\)  null-state can only be of type-1. Now suppose the \((\Delta =0,l=1)\)  null-state is the level-\(n\)  descendant of the \((\delta ,l^{\prime })\)  primary. Since \((\Delta =0,l=2)\)  is of type-1 we have,
\(\delta = 1- n - l^{\prime } , \quad \delta + n = \Delta = 0 , \quad n + l^{\prime } = 2\) 
